Math

Number Base Converter — Free 2026

Convert between binary, octal, decimal, and hexadecimal number systems instantly.

Input Value Invalid number for the selected base.

From Base

Conversion Results

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Binary (Base 2)

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Octal (Base 8)

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Decimal (Base 10)

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Hexadecimal (Base 16)

How It Works

Enter your number
Select the input base
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Understanding Number Systems

Number systems are the foundation of how we represent and manipulate quantities. While humans naturally count in decimal (base 10) because we have ten fingers, computers operate in binary (base 2) because their circuits have two states: on and off. Octal (base 8) and hexadecimal (base 16) serve as convenient shorthand for binary values, making it easier for programmers and engineers to read and write large binary numbers without error.

Each number system uses a fixed set of digits. Binary uses 0 and 1, octal uses 0 through 7, decimal uses 0 through 9, and hexadecimal uses 0 through 9 plus the letters A through F (where A = 10, B = 11, C = 12, D = 13, E = 14, F = 15). The base determines how place values increase from right to left: in decimal, each position is worth 10 times the previous; in binary, each is worth 2 times the previous.

Where Each Base Is Used

Binary is the native language of all digital electronics. Every piece of data — text, images, audio, video — is ultimately stored as sequences of binary bits. Hexadecimal is the most common human-readable representation of binary data. Web developers use it daily for colour codes (like #FF5733), and programmers use it for memory addresses, byte values, and debugging output. Octal is less common today but still appears in Unix file permissions (e.g., chmod 755) and some legacy systems. Decimal remains the universal system for everyday mathematics, commerce, and communication.

Conversion Methods

The standard method for converting between bases involves two steps: first convert the input to decimal (by multiplying each digit by its positional value and summing), then convert from decimal to the target base (by repeatedly dividing by the base and collecting remainders). This tool handles both steps automatically using JavaScript's built-in parseInt() and toString() methods, ensuring accurate conversions for integers up to the maximum safe integer value. For related mathematical tools, try our Roman numeral converter for historical number system conversions.

Frequently Asked Questions

How do I convert binary to decimal?

Each binary digit represents a power of 2, starting from the rightmost digit at 2^0. Multiply each bit by its power of 2 and sum the results. For example, binary 1010 = 1x8 + 0x4 + 1x2 + 0x1 = 10 in decimal.

What is hexadecimal used for?

Hexadecimal (base 16) is widely used in computing because each hex digit maps exactly to four binary bits, making it a compact way to represent binary data. Common uses include color codes in web design (#FF5733), memory addresses, MAC addresses, and byte values in programming.

What is the difference between binary, octal, decimal, and hexadecimal?

Binary (base 2) uses digits 0-1, octal (base 8) uses 0-7, decimal (base 10) uses 0-9, and hexadecimal (base 16) uses 0-9 and A-F. Decimal is the standard human numbering system, while binary is how computers store data internally. Octal and hex are shorthand notations for binary values.

Can I convert negative numbers between bases?

This converter handles positive integers. Negative numbers in computing are typically represented using two's complement notation, which depends on the bit width of the system (8-bit, 16-bit, 32-bit, etc.). For negative values, first convert the absolute value and then apply the appropriate signed representation for your use case.